{
  "id": "2003.05299",
  "version": "v1",
  "published": "2020-03-10T04:37:18.000Z",
  "updated": "2020-03-10T04:37:18.000Z",
  "title": "The N-vortex Problem on a Riemann Sphere",
  "authors": [
    "Qun Wang"
  ],
  "comment": "32 pages, 3 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "This article investigates the dynamical behaviours of the $n$-vortex problem with vorticity $\\mathbf{\\Gamma}$ on a Riemann sphere $\\mathbb{S}^2$ equipped with an arbitrary metric $g$. From perspectives of Riemannian geometry and symplectic geometry, we study the invariant orbits and prove that with some constraints on vorticity $\\mathbf{\\Gamma}$, the $n$-vortex problem possesses finitely many fixed points and infinitely many periodic orbits for generic $g$. Moreover, we verify the contact structure on hyper-surfaces of the vortex dipole, and exclude the existence of perverse symmetric orbits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-10T04:37:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76B47",
      "30F45",
      "37J45",
      "58E05"
    ],
    "keywords": [
      "riemann sphere",
      "n-vortex problem",
      "vortex problem possesses",
      "perverse symmetric orbits",
      "contact structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}